What is the Greatest Common Factor of 36000 and 36008?

Greatest common factor (GCF) of 36000 and 36008 is 8.

GCF(36000,36008) = 8

We will now calculate the prime factors of 36000 and 36008, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36000 and 36008.

How to find the GCF of 36000 and 36008?

We will first find the prime factorization of 36000 and 36008. After we will calculate the factors of 36000 and 36008 and find the biggest common factor number .

Step-1: Prime Factorization of 36000

Prime factors of 36000 are 2, 3, 5. Prime factorization of 36000 in exponential form is:

36000 = 2⁵ × 3² × 5³

Step-2: Prime Factorization of 36008

Prime factors of 36008 are 2, 7, 643. Prime factorization of 36008 in exponential form is:

36008 = 2³ × 7¹ × 643¹

Step-3: Factors of 36000

List of positive integer factors of 36000 that divides 36000 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 96, 100, 120, 125, 144, 150, 160, 180, 200, 225, 240, 250, 288, 300, 360, 375, 400, 450, 480, 500, 600, 720, 750, 800, 900, 1000, 1125, 1200, 1440, 1500, 1800, 2000, 2250, 2400, 3000, 3600, 4000, 4500, 6000, 7200, 9000, 12000, 18000

Step-4: Factors of 36008

List of positive integer factors of 36008 that divides 36000 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 643, 1286, 2572, 4501, 5144, 9002, 18004

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36000 and 36008. The biggest common factor number is the GCF number.
So the greatest common factor 36000 and 36008 is 8.

Also check out the Least Common Multiple of 36000 and 36008